15. (1/5)^(x-2) = 125 Вариант 7 1. 3^x = 81 2. 4^(x-1) = 64 3. 2^(3x) = 512 4. (1/7)^x = 49 5. 5^(x+3) = 125 6. 2^x = 1/128 7. (1/9)^(2x) = 81 8. 3^(x-4) = 81 9. 16^x = 64 10. (1/2)^x = 512 11. 3^(x-2) * 5^(x-2) = 45 12. 2^(5x-3) = 32 13. 7^(x+1) = 1/49 14. 4^x * 64 = 1024 15. (1/6)^x+1 = 36

Вариант 7

1. 3^x = 81

3^x = 3⁴

x = 4

Ответ: x = 4

2. 4^x-1 = 64

4^x-1 = 4³

x - 1 = 3

x = 4

Ответ: x = 4

3. 2^3x = 512

2^3x = 2⁹

3x = 9

x = 3

Ответ: x = 3

4. (1/7)^x = 49

(1/7)^x = (1/7)^-2

x = -2

Ответ: x = -2

5. 5^x+3 = 125

5^x+3 = 5³

x + 3 = 3

x = 0

Ответ: x = 0

6. 2^x = 1/128

2^x = 2^-7

x = -7

Ответ: x = -7

7. (1/9)^2x = 81

(1/9)^2x = (1/9)^-2

2x = -2

x = -1

Ответ: x = -1

8. 3^x-4 = 81

3^x-4 = 3⁴

x - 4 = 4

x = 8

Ответ: x = 8

9. 16^x = 64

(4²)^x = 4³

4^2x = 4³

2x = 3

x = 3/2 = 1.5

Ответ: x = 1.5

10. (1/2)^x = 512

(1/2)^x = (1/2)^-9

x = -9

Ответ: x = -9

11. 3^x-2 * 5^x-2 = 45

15^x-2 = 45

Тут, к сожалению, быстро не получится решить, нужен логарифм!

12. 2^5x-3 = 32

2^5x-3 = 2⁵

5x - 3 = 5

5x = 8

x = 8/5 = 1.6

Ответ: x = 1.6

13. 7^x+1 = 1/49

7^x+1 = 7^-2

x + 1 = -2

x = -3

Ответ: x = -3

14. 4^x * 64 = 1024

4^x * 4³ = 4⁵

4^x+3 = 4⁵

x + 3 = 5

x = 2

Ответ: x = 2

15. (1/5)^x-2 = 125

(1/5)^x-2 = (1/5)^-3

x - 2 = -3

x = -1

Ответ: x = -1